If `a(b-c)x^(2)+b(c-a)xy+c(a-b)y^(2)` is a perfect square, the quantities a,b,c are in

Show that If a(b-c) x^2 + b(c-a) xy + c(a-b) y^2 = 0 is a perfect square, then the quantities a, b, c are in harmonic progresiion

If the left hand side of the equation a(b-c)x^2+b(c-a) xy+c(a-b)y^2=0 is a perfect square , the value of {(log(a+c)+log(a-2b+c)^2)/log(a-c)}^2 , (a,b,cinR^+,agtc) is

If the expression a^(2)(b^(2)-c^(2))x^(2)+b^(2)(c^(2)-a^(2))x+c^(2)(a^(2)-b^(2)) is a perfect square, then

If (b+c-2a)/a , (c+a-2b)/b , (a+b-2c)/c are in A.P. , then a,b,c are in :

If the expression x^2+2(a+b+c)+3(b c+c+a b) is a perfect square, then a=b=c b. a=+-b=+-c c. a=b!=c d. non eoft h e s e

If x, a, b, c are real and (x-a+b)^(2)+(x-b+c)^(2)=0 , then a, b, c are in

If the roots of the equation (a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0 are equal, then (a) 2b=a+c (b) b^2=a c (c) b=(2a c)/(a+c) (d) b=a c

Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2 , B=b^2c+b c^2-a^2b-a b^2,and C=a^2c +'a c^2-b^2' c-b c^2, w h e r ea > b > c >0 and the equation A x^2+B x+C=0 has equal roots, then a ,b ,c are in AdotPdot b. GdotPdot c. HdotPdot d. AdotGdotPdot

If the lines (a-b-c) x + 2ay + 2a = 0 , 2bx + ( b- c - a) y + 2b = 0 and (2c+1) x + 2cy + c - a - b = 0 are concurrent , then the prove that either a+b+ c = 0 or (a+b+c)^(2) + 2a = 0

During the transformation of ._(c )X^(a) to ._(d)Y^(b) the number of beta -particles emitted are a. d + ((a - b)/(2)) - c b. (a - b)/(c ) c. d + ((a - b)/(2)) + c d. 2c - d + a = b